Quality and Reliability Engineering International, 14, 1998, 4
In many process monitoring situations where the data are collected over time, the measurements tend to be autocorrelated. In those cases one can fit a time series model to the data to account for the autocorrelation. Once a model has been fitted, it can be used to predict the behaviour of the process, and the residuals can be used to monitor the process using e.g., a Shewhart or Cusum chart. Two issues that are often overlooked when fitting time series models and using the residuals for process monitoring are (i) the validity of the underlying assumption that the time series model fitted to the data will also fit future observations reasonably well, and (ii) that its parameters will remain fairly constant. Either of these assumptions, or both, might not hold, which in turn will affect the performance of the monitoring scheme. In this paper we show how Cuscore charts can be used to check these assumptions by detecting changes in the parameters of an integrated moving average (IMA) model used to monitor the air quality in a clean room environment. The Cuscore can also be effectively used to detect non-stationarity in time series data as well as departures from a state of statistical control.